Research On Characteristics Of Complex Wave In The Two Dimensional Rectangular Functionally Graded Bar And Ring Waveguides

Functionally graded material(FGM),as a new type of composite material,is composed of two or more materials with continuous gradient changes.This distribution eliminates the complicated interface effect between different materials.The versatility of the material can be realized by changing the spatial distribution of the component content.Because of their unique properties,FGM has been used in the fields of shipbuilding,aviation,aerospace and nuclear energy.In nondestructive testing,ultrasonic guided waves are favored by researchers because of their advantages.They have long propagation distance,small attenuation,strong resolution and high sensitivity.With the progress of science and technology and the deepening of research,ultrasonic guided wave detection is not only limited to the location of defects,but also hopes to reconstruct the size and shape of defects.A complete guided wave consists of a finite number of propagating wave modes and an infinite number of evanescent wave modes.And then the evanescent wave modes has good resolution ability at the structure boundary or defect boundary.When the damping is small,the complex evanescent wave modes with small imaginary part wavenumber can travel a long distance Therefore,complex wave plays an important role in the detection of defect shape and size.At present,the research on the characteristics of two-dimensional waveguides are mainly about propagation waves.However,few researchers have studied evanescent waves,especially for the wave characteristics of FGM.The non-uniformity of FGM makes the calculation of wave characteristics more complicated and difficult.This paper presents an analytical method based on double-Legendre orthogonal polynomial series.Using this method to study propagating and evanescent wave in bars and ring with rectangular cross-section,especially the properties of evanescent waves.This method can transform the complex variable coefficient wave differential equation into an eigenvalue matrix equation whose eigenvalues are wavenumbers.When the frequency and step size of frequency is given,through this method can obtain pure real propagation wave,pure imaginary number of evanescent wave which present exponential decay,and complex numbers of evanescent wave which present sinusoidal decay.This method can avoid the shortcomings of the iterative methods such as many times of circulation,huge quantity of calculation,lower accuracy.Firstly,in the rectangular coordinate system,study the characteristics of guide waves in piezoelectric bar with rectangular section,FGM bar with rectangular section and FGPM bar with rectangular section.This paper studies the effect of piezoelectric,gradient function and aspect ratio on the characteristics of the guided wave.The analysis revealed that that both the imaginary part of complex wave and the cut-off frequency of propagation wave decrease with the increase of the width of rectangular bar,and decrease with the increase of gradient function exponential.Secondly,under the cylindrical coordinate system,using this method to study the characteristics of guide waves in piezoelectric ring with rectangular section,FGM ring with rectangular section and FGPM ring with rectangular section,especially the properties of complex waves.This paper studies the effect of piezoelectric,gradient function and diameter-thick ratio on the characteristics of the guided wave.Through research and analysis,it is found that the attenuation of complex wave increases with the increase of the diameter-thickness ratio.At high frequencies,the difference of the gradient function has a significant effect on the propagating wave and the complex wave.Furthermore,also found that piezoelectric property has a significant influence on pure imaginary modal.Finally,we build a FGM bar model through COMSOL finite element simulation software.By means of modal analysis,we extracted the characteristic frequency of the model and drew the dispersion curve.We compare the dispersion curve with that obtained by numerical calculation to verify the correctness of the method.